Running head: STUDY ON LINEAR ELASTIC FRACTURE MECHANICS LINEAR ELASTIC FRACTURE MECHANICS: DEVELOPMENT AND ADVANCEMENT IN STUDY OF CATASTROPHICS FAILURES & FRACTURE ANALYSIS Name of the student: Name of the university: Author note:
STUDY ON LINEAR ELASTIC FRACTURE MECHANICS1 Table of Contents Introduction:....................................................................................................................................2 Related theories:..............................................................................................................................3 Formulas and assumptions used in LEFM:.................................................................................3 Advantages and drawbacks..........................................................................................................4 Gradual development in this field:..................................................................................................5 Recent research work:......................................................................................................................6 LEFM Characterization of an Anisotropic Shale:.......................................................................6 Conclusion:......................................................................................................................................8 References:......................................................................................................................................9
STUDY ON LINEAR ELASTIC FRACTURE MECHANICS2 Introduction: Fracture is one of the most serious problems that the society has been facing from a very long time. Fractures have started occurring ever since the inception of manmade structures in the history of the world. The problem now is even worse than what is used to be centuries back since more and more technologies and advancement in manmade structures are coming up with increased complexities. Much research has been carried out in the past, which has only generalized the preexisting technologies. However not much research has been done on the specific trends of elastic fractures. This topic is extremely important to be further researched on. Different recommendations as well as feedbacks regarding minimizing catastrophic accidents in the future can be obtained. The different kinds of micro mechanisms that leads to the fracture failures can be understood with an in depth analysis of this topic (Kanget al.2015). The roles of “process zone” as well as the two dimensions of the fracture phenomena, which are deterministic and the probabilistic dimensions, can be addressed. Linear Elastic Fracture Mechanics or LEFM assumes the material to beisotropic as well as linear elastic in nature and based on this assumption, the field of stress by the side of the crack tip can be calculated using the elasticity theory. When the stresses in the crack tip area exceeds the toughness of the material fracture, the crack grows (Minhajuddin, Saha and Biligiri 2015). Most of the formulas are derived either for eitherplane stressorfor plane strains, which are associated with three loading modes of loadings on a body that is cracked:opening,sliding, as well astearing.
STUDY ON LINEAR ELASTIC FRACTURE MECHANICS3 Related theories: Formulas and assumptions used in LEFM: The basic analysis of LEFM is the stress in the area of the cracked tip. It is the location function, the conditions of loading conditions as well as the specimen geometry, which can be shown using the formula as shown below in the diagram. It is assumed that there is no stress intensity factor in the idea scenario. Figure 1: Basic analysis formula for LEFM(Wanhill, Molent and Barter 2013). However, in practice the stress intensity factor or “K” is calculated based on the crack tip stress and it is compared against the fracture toughness as a function of the location, loading as well as the geometry. The location is represented asrandis the coordinate system. Figure 2: Calculation of stress intensity factor “k” in LEFM(Weißgraeberet al.2016). The fracture toughness can be calculated using a material specific stress intensity factor Kc(Nejati, Paluszny and Zimmerman 2015). It is assumed that the stress intensity factororKis lesser thanKc.
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